Linear Phase Gradient Research Articles

Integer multi-wavelength gradient phase metagrating for perfect refraction: Phase choice freedom in supercella).

Phase gradient metagratings (PGMs) reshape the impinging wavefront though the interplay between the linear adjacent phase increment inside supercells and the grating diffraction of supercells. However, the adjacent phase increment is elaborately designed by tuning the resonance of each subcell at a certain target frequency, which inevitably confines PGMs to operate only at the single frequency in turn. We notice that there exists a freedom of phase choice with a multi-2π increment in a supercell of PGMs, whereas conventional designs focus on the 2π increment. This freedom can induce a collaborative mechanism of surface impedance matching and multi-wavelength subcells, enabling the design of PGMs at multi-wavelengths. We further design and fabricate a supercell consisting of eight curved pipes to construct the two-wavelengths PGMs. The linear adjacent phase gradient of 0.25π at the fundamental frequency 3430 Hz is achieved, while the almost perfect transmission effect is observed due to the impedance match at the ends of curved pipes. In addition, the transmission field at the double frequency 6860 Hz is measured, whose refraction direction is consistent with that at 3430 Hz. This design strategy originated from phase choice freedom in the supercell and the experimental fabrication might stimulate applications on other multi-wavelength metasurfaces/metagratings.

Acoustic metasurface development for transmitted wavefront manipulation using a level set-based topology optimization approach

A customized transmission-type metasurface design is developed for high-efficiency wavefront modulation by employing a level set-based topology optimization approach. The metasurface consists of periodically arranged supercells made of discrete unit cells aiming to form a precisely linear phase gradient of the transmitted wave ranging from 0 to 2π with high transmittances. The configuration of each unit is optimized to generate a desired phase and amplitude response of the transmitted wave at the interface. The transmitted wavefront steering realized by the phase-gradient metasurface is numerically and experimentally verified according to the diffraction theory, demonstrating that the level set-based topology optimization approach is a viable and effective technique for developing a transmitted phase-gradient metasurface. Afterwards, the designed optimal unit cells are elaborately arranged to form desired phase shift distributions for realizing fascinating acoustic functionalities, including acoustic energy focusing and acoustic Airy-like beam generation, further demonstrating the ability of the optimal units to achieve unprecedented transmitted wavefront control. This study presents a promising approach for customized transmission-type metasurface design based on the level set-based topology optimization, which is expected to be significantly valuable for acoustic device development.

Complex Refraction Metasurfaces for Locally Enhanced Propagation Through Opaque Media

AbstractMetasurfaces with linear phase gradients can redirect light beams. Controlling both phase and amplitude of a metasurface is proposed to extend Snell's law to the realm of complex angles, enabling a non‐decaying transmission through opaque media with complex refractive indices. This leads to the discovery of non‐diffracting and non‐decaying solutions to the wave equation in opaque media, in the form of generalized cosine and Bessel‐beams with a complex argument. While these solutions present nonphysical exponentially growing side tails, this is addressed via a windowing process, removing the side tails of the field profile while preserving significant transmission enhancement through an opaque slab on a small localized region. Such refined beam profiles may be synthesized by passive metasurfaces with phase and amplitude control at the opaque material's interface. The findings, derived from rigorous solutions of the wave equation, promise new insights and enhanced control of light propagation in opaque media.

Reconfigurable Wide‐Angle Beam‐Steering Terahertz Metasurfaces Based on Vanadium Dioxide

AbstractThe sixth generation (6G) wireless network is envisioned to provide faster and more reliable communication by utilizing electromagnetic waves in the terahertz spectrum. However, terahertz waves suffer from high propagation loss and, hence, wavefront manipulation solutions to focus and redirect terahertz waves are of paramount importance. Reconfigurable intelligent surface (RIS) is one such promising dynamic wavefront engineering solution proposed for 6G networks, but the technological realization of 6G (>100 GHz) RIS is still largely lacking. Here, spatially‐selective vanadium dioxide (VO2) patches incorporating coding metasurfaces for dynamic beam steering of terahertz waves are presented. The reversible and abrupt insulator‐to‐metal phase transition property of VO2 is exploited to achieve a reconfigurable transmission angle for the normal incident terahertz wave. By designing metasurfaces with specific linear phase gradients and designer phase sequencing, electrically switchable beam steering is achieved from co‐polarized 0° (normal transmission) in the OFF state to cross‐polarized 0° (control), 11°, 23°, 36°, and 52° in the ON state at 0.6 THz. Scaling up the proposed concept to achieve individual control of each active element (VO2) within the metasurface will enable a complete 6G RIS solution for full 3D terahertz beam manipulation to support the future THz wireless communication networks.

Efficient Anomalous Reflector Design Using Array Antenna Scattering Synthesis

A perfect anomalous reflector is designed by employing the receiving and scattering array antenna theory to optimize the scattering characteristics of a planar reflecting surface. For periodic reflectors with a supercell consisting of a relatively few reactively loaded radiating elements, reflection amplitudes into propagating Floquet modes are controlled in an algebraic optimization of the load reactances, avoiding brute-force optimization via electromagnetic simulations. Wide-angle reflectors are numerically designed and compared with the conventional reflectarray designs, showing that the proposed design approach achieves reflection efficiencies higher than the linear reflection phase gradient method in a computationally efficient manner.

Revealing a one-dimensional optically cloaked surface using the spin Hall effect of light.

The realization of an optical cloak that can hide a target object is no longer fiction, yet distinguishing the optically cloaked surface from our illusion remains an open problem. Here, the detection of a one-dimensional optically cloaked surface is presented by leveraging the spin Hall effect of light, the microscopic and transverse splitting of linearly polarized light at an optical interface into two circular polarizations. We first derive an analytical formula for the spin Hall shift at a planar surface with a linear phase gradient and demonstrate that the spin Hall effect of light at the cloaked surface differs from that at its perceived image. The theoretical description and numerical computation are generalized for a curved surface with a nonlinear phase gradient. Two approaches for examining optically cloaked surfaces are presented, in which the unknown incident angle and phase gradient are successfully reproduced. This work suggests the potential of the spin Hall effect of light in various applications, including anti-counterfeiting and security.

The exploration of transmission property by using the circular-interface types of porous acoustic metamaterials

Based on the generalised Snell’s law, many planar-interface types of acoustic metamaterials have been proposed and extensively used. However, circular-interface types of acoustic metamaterials (CAMs) that could be applied to aero-engine intakes and aircraft fuselages have not been extensively explored. Porous CAMs have been explored theoretically, numerically, and experimentally to investigate their acoustic properties, such as wave-front modulation and insertion loss, in this research. The analytical equation that governs the sound refraction of cylindrical waves through CAMs is derived based on the principle of stationary phase for the first time. In the numerical study, two types of porous CAMs with various geometries that generate periodically linear phase gradients are applied to circular interface structures. Results indicate that the excitation of high-order wave modes in the transmitted sound pressure field is dependent on the angular distance over one period of porous CAMs. When this parameter goes below critical values, the high-order wave modes in the transmitted sound pressure field will be converted into evanescent surface waves. Consequently, the sound insertion loss of porous CAM is significantly enhanced compared to that of uniform melamine foam of the same thickness. Based on the analytical and numerical study, technical guidance is proposed for designing porous CAMs with defined radii and dominant frequencies, taking compensation factors into account. This study offers a technical method for extending the industrial applicability of acoustic metamaterials from a planar interface to a circular interface.

Terahertz graphene metasurfaces for cross-polarized deflection, focusing, and orbital angular momentum.

Polarization is an important characteristic of electromagnetic wave. Due to novel optical properties, graphene-based anisotropic structure is widely used to control polarization state of electromagnetic wave. In this work, four graphene-based meta-atoms are designed to regulate polarization state of terahertz wave by changing Fermi energy level of graphene. When Fermi energy level is 0.01 eV, cross-polarized wave is emitted by four meta-atoms with phase difference of 90° at 1.18 THz, and the corresponding polarization conversion ratio reaches ∼90%. When Fermi energy level is adjusted to 0.70 eV, linear phase gradient will disappear, and cross-polarized wave almost disappears. Using four selected elements, three dynamic metasurfaces are designed for controlling wavefront of reflected beam, and they are gradient metasurface, metalens, and vortex beam generator. The designed metasurfaces successfully combine wavefront control and polarization manipulation, and greatly improve the ability to control electromagnetic wave. Our designs may have many potential applications, such as terahertz switching, imaging, and polarization beam splitter.

Design of broadband achromatic metasurface device based on phase-change material Ge2Sb2Te5

Based on the phase-change material Ge2Sb2Te5 (GST), achromatic metasurface optical device in the longer-infrared wavelength is designed. With the combination of the linear phase gradient GST nanopillar and the adjustment of the crystalline fraction m value of GST, the polarization insensitive achromic metalenses and beam deflector metasurface within the longer-infrared wavelength 9.5 μm to 13 μm are realized. The design results show that the achromatic metalenses can be focused on the same focal plane within the working waveband. The simulation calculation results show that the full-width at half-maximum (FWHM) of the focusing spot reaches the diffraction limit at each wavelength. In addition, the same method is also used to design a broadband achromatic beam deflector metasurface with the same deflection angle of 19°. The method proposed in this article not only provides new ideas for the design of achromatic metasurfaces, but also provides new possibilities for the integration of optical imaging, optical coding and other related optical systems.

On the role of spatial dispersion in boundary conditions for perfect non-specular reflection

Exact solutions for perfect anomalous reflection through metasurfaces have been recently developed in terms of both ideal nondispersive impenetrable boundary conditions (BCs) and penetrable BCs on top of a grounded slab. The second model is more accurate for the description of metasurfaces realized in PCB technology. Focusing on this particular class of metasurfaces, this paper investigates the connection between the two solutions, with the aim to clarify the role of spatial dispersion. It is shown that the two solutions can be related through an equivalent transmission network where transmission lines with different wavenumbers are associated to the incident and reflected waves. Finally, numerical analyses are carried out to assess the impact of neglecting spatial dispersion, as it is done in designs based on a linear phase gradient of the local reflection coefficient.

Cylindrical vector beam sorter with spin-dependent spiral transformation.

Here, we propose and experimentally demonstrate a cylindrical vector beam (CVB) sorter based on a spin-dependent spiral transformation. By exploiting the spin-orbital interaction of the geometric phase, a pair of conjugated spiral transformations are applied to modulate the two orthogonal circularly polarized components of the CVB, which are converted into the same linear phase gradient from opposite azimuthal phase gradients. Since the orthogonal spin components of CVBs with different polarization orders carry different phase gradients, under the convergence of a convex lens, the coaxially transmitted CVBs can be sorted with spatially separated positions, and the increased phase gradient provided by the spiral transformation yields the high resolution. We show that five CVB modes from -2 to +2 are successfully sorted with a separation efficiency of 3.65. As a proof-of-concept, we demonstrate a two-channel CVB multiplexing communication with a bit error rate approaching 10-6. In addition to providing an avenue for CVB demultiplexing, our results show potential applications in mode filtering and mode routing in all-optical interconnection.

Broadband continuous beam-steering with time-modulated metasurfaces in the near-infrared spectral regime

A time-modulated metasurface integrated with indium-tin-oxide (ITO) can dynamically manipulate the scattered light by imparting dispersionless phase discontinuities with 2π span on wavefronts of the generated sidebands. However, maximal frequency conversion efficiency is restricted to a narrow bandwidth at the vicinity of the resonant wavelength due to the dispersive nature of light–matter interactions in such ITO-integrated metasurfaces. Herein, a multiwavelength time-modulated meta-molecule is numerically investigated, which consists of four metal–insulator–metal meta-atoms that are judiciously designed to support four resonant wavelengths at the near-infrared regime. The metasurface platform allows for application of four sets of independent radio-frequency signals to each meta-molecule, which are optimized to excite the output spectra with dominant first-order up-modulated sidebands. Individual modulation of each meta-atom leads to efficient sideband generation at resonant wavelength corresponding to the biased meta-atom. Nevertheless, the conversion efficiency decays rapidly at off-resonant wavelengths. Concurrent modulation of all four meta-atoms within the meta-molecule configuration offers a pathway to simultaneously generate dominant sidebands at all resonant wavelengths while enhancing the frequency conversion efficiency at inter-resonant wavelengths. As the potential application, beam-steering at the up-modulated sideband by both individually and simultaneously biased meta-atoms is demonstrated. It is revealed that simultaneous modulation enables continuous dynamic light deflection over a broad spectrum spanning on 1–1.8 μm, while the steering angle of the wavelengths changes in the range of 34°–85°. Broadband continuous beam-scanning is a non-trivial task that cannot be accomplished by a quasi-static metasurface relying on dispersive resonant phase shift, which hinders simultaneous implementation of linear phase gradients at all incident wavelengths.

Self-complementary metasurfaces for designing terahertz deflecting circular-polarization beam splitters

Metasurfaces provide a broad range of functionalities related to wavefront manipulation in different frequency ranges with the advantage of subwavelength thickness. In this work, we numerically and experimentally investigate a terahertz splitter of circularly polarized beams based on a spatially nonuniform metasurface composed of self-complementary unit cells. When illuminated with circular polarization, the metasurface creates a deflected cross-polarized beam while transmitting a co-polarized beam in the normal direction. Despite the existence of two reflected beams leading to reflective losses, the metasurface is single-layer and is easy to design and fabricate. A required linear phase gradient for the cross-polarized beam can be obtained by adjusting only one design parameter of unit cells.

Quasi-continuous linear phase-gradient metamaterial based on conformal spoof surface plasmon polaritons

In this work, we propose a method of achieving quasi-continuous linear phase gradient for transmitted waves based on conformal spoof surface plasmon polariton (SSPP). To this end, a SSPP structure with high transmission is firstly designed as the unit cell of the metamaterial. To obtain the phase gradient, SSPP structures are arranged delicately in a way that they are conformal to the brachistochrone curve. In this way, quasi-continuous linear Pancharatnam-Berry (PB) phase profile can be realized strictly along one of the two transverse directions. To verify this idea, a dual-band transmissive metamaterial operating in X and Ku band was designed, fabricated and measured. Due to the phase gradient imparted by the conformal SSPP structures, high-efficiency anomalous refraction can be realized within the two bands. Different from the general PGM, the phase gradient of the conformal SSPP structure allows us to achieve the desired anomalous refraction angle without reconstructing the PB phase. Both the simulation and measurement results are well consistent with theoretical predictions. This work provides another strategy of achieving anomalous refraction and may find applications in beam steering, digital beam forming, etc.

Design of Compact Terahertz Surface Plasmon Polaritons Devices

A slot-antenna-based device which can stimulate terahertz surface plasmon polaritons (SPPs) and control the wave front of the SPPs simultaneously has been designed and fabricated. The device is constituted of H-shaped-slot antennas. By adjusting the geometric parameters of antennas, the grouped structure can provide a linear phase gradient which will improve the conversion efficiency of the terahertz propagating wave into the surface wave. The phase of the converted surface wave can be adjusted by changing the order of the slot antennas in each group, such the wave front of the surface wave can be modulated simultaneously. A terahertz SPPs lens is designed and fabricated based on this approach. Experimental results demonstrate the validity of the proposed method. This approach can significantly simplify the design and fabrication of most integrated SPPs devices and may pave the avenue for developing complex SPPs devices.

Point to point propagation over a phase gradient grooved surface

Previous work on deriving a modal theory for predicting point-to-point propagation over a uniformly grooved surface is extended to predict propagation over a periodic variable depth grooved surface with a low flow resistivity porous material of different thickness in each groove. The form of the surface is intended to create an approximately linear phase gradient for plane waves reflected from the surface. The resulting attenuation due to ground effect is found to be larger and more broadband than predicted over either an acoustically hard grooved surface or an acoustically soft layer with thickness equal to the largest groove depth for the same source-receiver geometry. Various contributions to the excess attenuation spectrum from surface waves associated with the different groove depths, quarter wavelength resonances in the grooves, the phase gradient for plane wave reflections and diffracted modes are investigated. As result the broadband nature of the excess attenuation is explained and important parameters in designing such surfaces are identified.

Tunable beam splitter using bilayer geometric metasurfaces in the visible spectrum.

Metasurfaces have been widely investigated for their capabilities of manipulating wavefront versatilely and miniaturizing traditional optical elements into ultrathin devices. In this study, a nanoscale tunable beam splitter utilizing a bilayer of geometric metasurfaces in the visible spectrum is proposed and numerically examined. Inspired by the diffractive Alvarez lens and multilayer geometric metasurfaces, opposite quadratic phase distributions are imparted on both layers, and a varying linear phase gradient will arise through relatively lateral displacement between two layers, generating tunable angles of deflection. In addition, such geometric metasurfaces offer opposite directions of phase gradients for orthogonal circularly polarized incidences, leading to effective polarization beam splitting. Results prove that the splitting angles can be tuned precisely, and the energy split ratio can be effectively changed according to the ellipticity of the polarized incidence. This design could find significant applications in optical communication, measurement, display, and so on.

Characterization of gap-plasmon based metasurfaces using scanning differential heterodyne microscopy

Optical phase-gradient metasurfaces, whose unique capabilities are based on the possibility to arbitrarily control the phase of reflected/transmitted light at the subwavelength scale, are seldom characterized with direct measurements of phase gradients. Using numerical simulations and experimental measurements, we exploit the technique of scanning differential heterodyne microscopy (SDHM) for direct phase and amplitude characterization of gap-plasmon based optical metasurfaces. Two metasurface configurations utilizing the third-order gap surface plasmon (GSP) resonance, representing a binary grating and linear phase gradient, are experimentally characterized with the SDHM operating at the light wavelength of 633 nm. Comparing the experimental performances of these GSP metasurfaces with those expected from the phase and amplitude profiles reconstructed from the SDHM measurements, we verify the efficiency and accuracy of the developed SDHM characterization approach for direct inspection of GSP reflective metasurfaces.

Wide-spatial scattering and arbitrary-angular tunability based on hybridized phase gradients from metasurface hologram algorithm

Light steering and wavefront shaping by metasurfaces typically relies on the elaborate phase arrangement from discrete plasmonic or dielectric resonators. A linear phase gradient profile could simply enable the beam bending (anomalous reflection/transmission) functionality. Comparing to the single beam steering performance, the applicable wide-scattering property is also highly in demand for more practical applications of full-spatial imaging and detection, etc. However, it is still challenging to come up with an efficient design route to manipulate the arbitrary wide-spatial scattering and complex phase gradient hybridization. Here, we propose a metasurface design route that could arbitrarily expand the visible-frequency light scattering into wide outgoing directions. An inverse-design metasurface based on hologram algorithm is created to form the complex phase gradient hybridization and realize wide-spatial scattering covering the outgoing angle range between ±60°. Such design method can also tailor to the arbitrary angular scattering functionality to outgoing angular direction at 15°–30°, 30°–45°and 45°–75°, respectively. Additionally, the proposed architecture operates at broadband visible wavelength rather than a single wavelength, and it also enjoys the robust optical scattering performance which is irrelevant to the incident angle variation. Overall, the presented design route is universal and can easily find applications for optical diffuser, light coupling/de-coupling, directional optical emitter, full-spatial imaging, light trapping and spectrum splitting, etc.

Dual-Band Beam-Scanning Antenna Using Rotatable Planar Phase Gradient Transmitarrays

A design of dual-band beam-scanning antenna using rotatable planar transmitarrays (TAs) is proposed in this communication. The antenna is composed of a dual-band lens and a pair of linear phase gradient (PG) TAs. The presented anisotropic lens is polarization independent, operating at two frequency bands. The PG TA is implemented by using double square loop units with different PGs at two frequencies. Two rotatable PG TAs are located above and parallel to the dual-band lens, and beam scanning in the upper hemisphere is achieved by rotating the two PG TAs synchronously around the axis orthogonal to the planes of the PG TAs. The procedure is demonstrated for dual-band beam-scanning implementation operating in linear polarization at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> - and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Ku$ </tex-math></inline-formula> -band. The full-wave simulation results demonstrate that the designed antenna enables beam steering in both azimuth and elevation planes at 8 and 14 GHz, with a peak gain of 16.7 and 19.8 dB in the broadside direction, respectively. Moreover, a prototype is fabricated, and the measured results confirm the feasibility of using this method for achieving low-cost lightweight, simple configuration dual-band 3-D coverage beam-scanning antenna.